A recipe for 1 gallon of fruit punch calls for 3/4 cup of orange juice. How many cups of orange juice are needed to make 8 gallo
1 answer:
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Answer:
475 transistors, 25 resistors and 50 computer chips can be produced.
Step-by-step explanation:
Let us consider, p = Number of transistors.
q = Number of resistors.
r = Number of computer chips.
The following three linear equations according to question,
The matrix form of any system, Ax = B
Where, A = Coefficient matrix
B = Constant vector
x = Variable vector
The inverse matrix, can be found by using the following formula,
Where, det A = Determinant of matrix A.
= Matrix of cofactors of A
Now, applying this formula to find ;
Here, , thus the matrix is invertible.
So, p = 475, q = 25, r = 50.
Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
